In the field of photonic crystals—artificial materials that possess a periodicity on the order of an optical length scale, the structural disorder is a problem in many cases as it scatters light randomly. While defects can be intentionally introduced in photonic crystals for light localization, random scattering of light in photonic crystals is in general a consequence of fabrication errors. However, curiously, many photonic patterns found in animals and plants are not perfectly periodic. For example, butterfly wings, humming birds, or blue Pollia fruits generate iridescent colors by employing periodic structures but the structures involve a degree of disorder that is much greater than that in typical photonic crystals fabricated by current nanopatterning techniques. If the structures in nature have been optimized, as generally thought, over hundreds of million years of evolution for various purposes such as signaling, mating, camouflage, and seed dispersing, it may suggest that a certain degree of structural randomness is actually not only favorable but even required for the best optical performance in many applications.
When structural randomness is present, light propagation can be divided into two modes: direct propagation and random scattering. The random scattering resembles diffusive transport of particles in many respects. In the diffusion picture of light propagation, energy packets are considered to perform a random walk due to the irregular structures. An important parameter in this picture is the transport mean free path, l*, which is defined as the average distance that an energy packet travels before its propagation direction has no correlation with its original direction. The transport mean free path is to be distinguished from the scattering mean free path, l, which is the average distance over which light propagates without scattering. Therefore, l* is larger than l and they are closer to each other as the scattering of a constituent particle is stronger. While the diffusion picture considers the transport of energy packets only, the wave nature of light such as interference is still preserved in random media. For example, back scattered light interferes always constructively and multiply scattered light can be localized in strongly scattering media due to interference, a phenomenon known as Anderson localization. In the embodiments of the present invention, the scattering, in most instances, will not be very strong, so that kl>>1, where k=2πn/λ with λ the wavelength of light in free space and n the average refractive index of the random media. Therefore, the light transport in the proposed work is well described by the diffusion picture.
Materials can cool under direct sunlight even below an ambient temperature. The cooling effect is achieved by minimizing solar absorption and maximizing heat radiation into an atmospheric window which is mostly within 8-13 μm in light wavelength. Prior art in a patent US 2014/0131023 achieved the cooling effect using multilayer structures. However, in these structures, the thickness of each layer needs to be precisely controlled within a few nanometers to efficiently block sunlight absorption. The sunblock performance of these structures degrades when applied to surfaces of high curvatures. Moreover, for practical applications, the fabrication of many layers over a large area presents manufacturing challenges in terms of throughput and cost. In comparison, paint-based coatings are much more convenient and cost-effective. Paints can be applied on highly curved surfaces without loss in cooling performance. Further, no precision control is required in applying paints on surfaces.
Solar heat preventive paints are typically based on particles of silica, borosilicate, titania, etc. While pigments that are non-white and highly reflective in near-infrared (IR) are used to reduce solar heating, these pigments are absorptive in the visible spectrum and hence less effective in cooling. For white paints, when the pigments are made of low refractive index materials such as silica, the particles are of a hollow spherical shell shape to enhance sunlight scattering. As in a U.S. Pat. No. 7,503,971, these particles are typically large compared to solar spectral wavelengths and ranges from 20 to 150 μm in size. As the particle size is large, the sunlight scattering efficiency is low and thick coatings are required to efficiently block sunlight. For high refractive index particles such as titania, current paint technology has determined that the particle size should be close to 200-250 nm to maximize whiteness of coatings.1, 2 While this size maximizes the scattering of visible wavelengths, these coatings suffer from solar heating due to weak scattering of near IR. Even commercial solar IR-blocking paints use particles of 200-250 nm in size.